Question

In the classic model given the following:

Production function: Y=3 K^.5 L^.5

Labor (L) is 400 units

Capital (K) is 100 units

Taxes (T) are 200

Government Spending (G) is 100

Marginal Propensity to Consume is .6

Investment is determined by the following function: I(r) = 1000- 100r where r is real interest rate.

1. a) If Government spending increases to 150, Investment and Savings and the interest rate will change. By how much? b) Output, Taxes and Consumption will not change. Briefly explain why not.

2) If Taxes increase (assuming Government spending is back to 100), will the following increase, decrease or stay the same? Y, C, Private S, Public S, National S, I and r.

Answer 1

(1)

(a) Y = 3 x (100)^0.5 x (400)^0.5 = 3 x 10 x 20 = 600

Consumption: C = a + b(Y - T) where a: Autonomous consumption, b: MPC

In equilibrium, Y = C + I + G = a + b(Y - T) + I + G

Y = 0 + 0.6(Y - 20) + 1000 - 100r + 100 [Autonomous consumption is not given, so we assume it is zero]

Y = 1,100 + 0.6Y - 120 - 100r

(1 - 0.6)Y = 980 - 100r

0.4Y = 980 - 100r

0.4 x 600 = 980 - 100r

240 = 980 - 100r

100r = 740

r = 7.4

C = 0.6 x (600 - 200) = 0.6 x 400 = 240

I = 1,000 - (100 x 7.4) = 1,000 - 740 = 260

Private saving = Y - C = 600 - 240 = 360

Public saving = T - G = 200 - 100 = 100

National saving = Private saving + Public saving = 360 + 100 = 460

When G increases to 150,

Y =0.6(Y - 20) + 1000 - 100r + 150

Y = 1,150 + 0.6Y - 120 - 100r

(1 - 0.6)Y = 1,030 - 100r

0.4Y = 1,030 - 100r

0.4 x 600 = 1,030 - 100r

240 = 1,030 - 100r

100r = 790

r = 7.9 (Increase by (7.9 - 7.4) = 0.5%)

C = 0.6 x (600 - 200) = 0.6 x 400 = 240

I = 1,000 - (100 x 7.9) = 1,000 - 790 = 210 (Decrease by (260 - 210) = 50)

Private saving = Y - C = 600 - 240 = 360 (Unchanged)

Public saving = T - G = 200 - 150 = 50 (Decrease by (100 - 50) = 50)

National saving = Private saving + Public saving = 360 + 50 = 410 (Decrease by (460 - 410) = 50).

(b) Output being a function of K and L whose values are given, will not change if G increases. Tax is autonomous, so is independent of G and will not change. Consumption is a function of MPC, Y and T which are independent of G, so C will not change.

(2) When T increases, ceteris paribus:

(i) Y being a function of K and L whose values are given, will not change if T increases.

(ii) C being inversely related to T, an increase in T will decrease C.

(iii) Decrease in C will increase private saving.

(iv) Increase in T will increase public saving.

(v) Increase in private saving and public saving will increase national saving.

(vi) A decrease in C, value of Y and G remaining unchanged, will increase I to keep the accounting equation balanced.

(vii) Increase in I will increase r.